RTF stock is expected to return 10.6 percent if the economy booms and only 4.2 percent if the economy goes into a recessionary period.The probability of a boom is 55 percent while the probability of a recession is 45 percent.What is the standard deviation of the returns on RTF stock?
A)4.03 percent
B)2.97 percent
C)3.18 percent
D)3.69 percent
E)5.27 percent

Question

Quizplus · Accepted Answer

The standard deviation can be calculated using the following formula:

σ = √[(p1 x r1^2) + (p2 x r2^2) - μ^2]

where:
p1 = probability of a boom = 0.55
p2 = probability of a recession = 0.45
r1 = return in a boom = 10.6%
r2 = return in a recession = 4.2%
μ = expected return = (p1 x r1) + (p2 x r2) = (0.55 x 10.6%) + (0.45 x 4.2%) = 7.56%

Substituting the values, we get:

σ = √[(0.55 x 10.6%^2) + (0.45 x 4.2%^2) - 7.56%^2]
σ = 3.18%

Therefore, the answer is C (3.18 percent).

RTF Stock Is Expected to Return 10